A few thousand people have rallied in the eastern Ukrainian city of Donetsk in support of pro-Russian separatists forced there by the advancing Ukrainian Army.

Pavel Gubarev, the self-styled governor of the self-declared "Donetsk People's Republic," told supporters in Donetsk's central square on July 6 that "we will begin a real partisan war around" the city of Donetsk.

Igor Girkin, aka Strelkov, told Russia's Life News that the separatists will "continue the combat operations [from Donetsk] and will try not to make the same mistakes we made in the past."

Girkin is known as the "defense minister" of the self-proclaimed people's republic and was based in the nearby city of Slovyansk until being flushed out along with hundreds of rebel fighters by Ukrainian military forces on July 5.

Fresh off its retaking of the large cities of Slovyansk and Kramatorsk, Ukrainian Defense Minister Valeriy Heletey said on July 6 that Ukrainian forces were also in control of Artyomovsk and Druzhkovka, previously held by the rebels.

Heletey, who assumed his post last week, was in Slovyansk shortly after the military regained control of it and was shown on television speaking with Ukrainian President Petro Poroshenko.

He said Poroshenko told him the government's priority was to rebuild damaged infrastructure in the region and to reconnect vital utilities.

Poroshenko has called the retaking of Slovyansk a "turning point" in Ukraine's battle against the rebels but said the army operation to "liberate the Donetsk and Luhansk regions will continue."

"My order is now in effect - tighten the ring around the terrorists," Poroshenko tweeted on July 6.

Prime Minister Arseniy Yatsenyuk ordered government officials to restore the work of the police, justice system, medical, and sanitary agencies as soon as possible.

The comments came shortly after government forces hoisted the national flag over Slovyansk after flushing them out of the industrial city in overnight fighting.

There were several reports of scores of militants killed and injured in the fighting, with the rebels fleeing the city and nearby regions and heading toward Donetsk.

Interior Minister Arsen Avakov said in a Facebook post that the militia fighters were also fleeing to Horlivka, a city of 260,000 about 50 kilometers southeast of Slovyansk that remains largely under the militia's control.

The routing of the rebels in Slovyansk is Kyiv's biggest success of its nearly three-month campaign to regain control of separatist-held parts of its eastern region.

Meanwhile, Donetsk billionaire businessman Rinat Akhmetov said the Ukrainian military must not bomb the city of Donetsk, where most of the ousted fighters from Slovyansk are believed to have fled to.

He said the Donbas region must remain part of a "united Ukraine" but said Donetsk, nearby settlements, and the surrounding infrastructure "must not be destroyed" by the Ukrainian military in its fight against the separatists.

The self-declared chairman of the "Donetsk People's Republic," Denis Pushilin, said on July 6 from an undisclosed location in Russia that the "peacemaking activities of the Russian Federation would be more than to the point right now."

Pushilin, who one day earlier had criticized Russia for not coming to the separatists' aid, added in an interview with Russia's Dozhd TV that he had met with Russian ultranationalist politician Vladimir Zhirinovsky.

He said Zhirinovsky was helping to secure "humanitarian aid" for the Donbas region.

Meanwhile, fresh fighting was reported on the outskirts of the city of Luhansk, capital of the Luhansk region.

Luhansk Mayor Volodymyr Pavlenko earlier said days of massive shelling and air strikes by the army led to fighters abandoning the strategically important eastern city.

Rebel leaders said the militia had withdrawn but was not beaten.

"Our resistance is not broken," said rebel leader Andrei Purgin, a leader in the self-declared "Donetsk People's Republic."

He told Interfax the fighters only left the city in order to protect the civilian population.